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The number of real solutions of the equa...

The number of real solutions of the equation `tan ^(-1) sqrt(x(x+1))+sin ^(-1) sqrt(x^(2)+x+1)=(pi)/(2)` is

A

two

B

one

C

zero

D

infinitely many

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The correct Answer is:
A
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HIMALAYA PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTION BANK
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  4. If sin ^(-1) (1)/(3)+sin ^(-1) (2)/(3)=sin ^(-1) x, then x=

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  5. If tan ^(-1) x+tan ^(-1)(1-x)=tan ^(-1) (4)/(3) then x=

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  6. If sin ^(-1) 2 x=cos ^(-1) x, then x=

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  7. The equation sin ^(-1) x-cos ^(-1) x=cos ^(-1) (sqrt((3))/(2)) has

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  8. The equation 2 cos ^(-1) x+sin ^(-1) x=(11 pi)/(6) has

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  9. If sin ^(-1) x+cos ^(-1)(1-x)=0 then x=

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  10. Considering only the principal values, if tan ("cot"^(-1) x)=sin ("cot...

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  11. If 2 tan ^(-1) (1)/(2)+sin ^(-1) x=(pi)/(2) then x=

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  12. The only integer (s) satisfying sin ^(-1) x+sin ^(-1)(1-x)=cos ^(-1) x

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  13. sin ^(-1) (5)/(x)+sin ^(-1) (12)/(x)=(pi)/(2) then x=

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  14. If cos^(-1) x = cot^(-1) ""4/3 + tan^(-1)""1/7, the x =

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  15. If 3 tan ^(-1)((1)/(2+sqrt(3)))-tan ^(-1) (1)/(x)=tan ^(-1) (1)/(3) th...

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  16. Solution of tan ^(-1)(1+x)+tan ^(-1)(1-x)=(pi)/(2) is

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  18. The value of tan^(2) (sec^(-1) 2) + cot^2 ("cosec"^(-1) 3) is :

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  19. The value of , sec ^(-1)((x)/(a))-sec ^(-1)((x)/(b))=sec ^(-1) b-sec...

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  20. sin ^(-1)[cos (sin ^(-1) x)]+cos ^(-1)[sin (cos ^(-1) x)]=

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